Perimeter.cptstubing said:Homework Statement
A rectangular region of 125,000 sq ft is fenced off. A type of fencing costing $20 per foot was used along the back and front of the region. A fence costing $10 per foot was used for the other sides. What were the dimensions of the region that minimized the cost of the fence?
Homework Equations
A=l*wThe Attempt at a Solution
I haven't a clue where to begin with this. What should I be thinking?
SammyS said:Perimeter.
Think Perimeter.
What's the perimeter of a rectangle?cptstubing said:I know this question should eventually look like a regular function like the practice questions I've been doing for ages, but I'm failing to see how I get there.
SteamKing said:What's the perimeter of a rectangle?
You have two dimensions to work with, length and width.
cptstubing said:L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.
SteamKing said:For right now, forget about the area of the rectangle. That comes later.
If you have a rectangle, any rectangle, with a length L and a width W, what is the formula for the perimeter of this shape?
cptstubing said:L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.
Ray Vickson said:When you write L*W, what do you mean? What is L? What is W? So, if you did know L and W, what other aspects of the fencing could you compute using those values?
You know the two variables -- L and W. You just don't happen to know their values. Even so, you should be able to write one expression that represents the perimeter of the fence, and another that represents the cost of that fence.cptstubing said:L*W means Area, or 125000. Length * Width. If I knew the two variables, I'd know the perimeter.
Mark44 said:You know the two variables -- L and W. You just don't happen to know their values. Even so, you should be able to write one expression that represents the perimeter of the fence, and another that represents the cost of that fence.
That's a good start.cptstubing said:P=(L*2)+(W*2)
Cost =(L*2*10)+(W*2*20)
I don't know if this is correct.
Forget process -- what you need to do is think about this problem.cptstubing said:What is I need to know before I can do this? A process or something?
That's $20 and $10 per foot. It's not per square foot .cptstubing said:L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.
cptstubing said:P=(L*2)+(W*2)
Cost =(L*2*10)+(W*2*20)
I don't know if this is correct. What is I need to know before I can do this? A process or something?
A critical point of a polynomial function is a point where the derivative of the function is equal to zero. It can also be defined as a point where the slope of the function changes from positive to negative or vice versa.
To determine the critical points of a polynomial function, you need to find the derivative of the function and set it equal to zero. Solve for the values of x that satisfy this equation to identify the critical points.
Critical points are important in polynomial functions because they can help us identify the location of local extrema (maximum or minimum points) on the graph of the function. They can also tell us about the behavior of the function and its concavity.
Yes, it is possible for a polynomial function to have multiple critical points. This can happen when the function has multiple terms or when it has a high degree. Each critical point can represent a change in the slope of the function.
To graph a polynomial function using critical points, you can plot the critical points on the graph and use them to determine the behavior of the function in between. You can also use the critical points to help you sketch the general shape of the curve and identify any local extrema.